Sharp asymptotics of the quasimomentum
Abstract
We consider the Schrödinger operator with a periodic potential $p$ on the real line. We assume that $p$ belongs to the Sobolev space $\mH_m$ on the circle for some $m\ge -1$, and we determine the asymptotics of the quasimomentum and the Titchmarsh-Weyl functions, the Bloch functions at high energy.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2011
- DOI:
- 10.48550/arXiv.1110.4716
- arXiv:
- arXiv:1110.4716
- Bibcode:
- 2011arXiv1110.4716K
- Keywords:
-
- Mathematics - Spectral Theory;
- 34L40;
- 30C20;
- 47E05
- E-Print:
- 16 pages, 3 figures, keywords: quasimomentum, integrated density of states, periodic potential